This is a very good question, and well done for noticing the details at the end which are definitely very strange and not explained to us. Firstly, I think the short answer to your question is that we do not know. We are not told whether Norma Jean killed herself. All we are told is that as she reaches the bluff overlooking the Tennessee River, she makes a gesture that Leroy is unable to interpret:

Norma Jean has reached the bluff, and she is looking out over the Tennessee River. Now she turns toward Leroy and waves her arms. Is she beckoning to him? She seemes to be doing an exercise for her chest muscles. The sky is unusually pale--the colour of the dust ruffle Mabel made for their bed.

The way in which the ending refers to the "pale" sky would perhaps indicate some kind of tragedy is about to occur, but we are not told if that involves Norma Jean's suicide. However, your question does draw attention to the way in which the text is filled with references to death. The most obvious example is of course the way that the death of Norma Jean and Leroy's marriage occurs on the site of the Shiloh battlefield. As Leroy tries to take in Norma Jean's words about the end of their marriage, he interestingly "tries to focus on the fact that thirty-five hundred soldiers died on the grounds around him." These deaths only serve to highlight the many deaths that are present in this excellent short story: the death of traditional gender roles, the death of former identities, and then, ultimately, the death of their relationship.